{"ID":6497562,"CreatedAt":"2026-07-13T01:19:40.13847098Z","UpdatedAt":"2026-07-14T01:36:59.12045529Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09662","arxiv_id":"2607.09662","title":"PHINN-EEG: Topological Time-Series Analysis of Dream-State EEG -- Dynamic Betti Curves for Dream Content Classification and Topology-Conditioned Neural Signal Synthesis","abstract":"Current electroencephalography (EEG)-based dream detection relies on power spectral density (PSD) and statistical moment features, achieving a state-of-the-art area under the receiver operating characteristic curve (AUC) of approximately 0.70 on the DREAM database (Wong et al., 2025, Nature Communications). We introduce PHINN-EEG (Persistent Homology Inspired Neural Network for EEG), the first topological time-series framework for dream mentation analysis. Using sliding-window Takens delay embeddings and Vietoris-Rips filtrations on multichannel pre-awakening EEG epochs, we extract Dynamic Betti Curves that characterize the geometric architecture of neural activity, not merely its energy. These topological invariants, combined with topology-conditioned flow matching, are analytically projected to outperform existing PSD and catch22 benchmarks, targeting AUC = 0.82-0.90 on the 1,462-awakening open-access subset of the DREAM database (drawn from a full registry of 3,191 total awakenings from 263 participants across 20 independent laboratories). We further introduce a topology-conditioned rectified flow model for dream-state EEG synthesis-with a spectral-conditioned flow model of comparable feature dimensionality as an additional ablation baseline to isolate the value of topological conditioning specifically-and propose a set of candidate Betti transition archetypes linking topology to phenomenological dream report categories, presented as an exploratory hypothesis space pending empirical validation. If validated, this work represents a paradigm shift from spectral energy to phase-space geometry in neural rare-event detection, with potential future implications for wearable BCI dream monitoring.","short_abstract":"Current electroencephalography (EEG)-based dream detection relies on power spectral density (PSD) and statistical moment features, achieving a state-of-the-art area under the receiver operating characteristic curve (AUC) of approximately 0.70 on the DREAM database (Wong et al., 2025, Nature Communications). We introduc...","url_abs":"https://arxiv.org/abs/2607.09662","url_pdf":"https://arxiv.org/pdf/2607.09662v1","authors":"[\"Ren Takahashi\",\"Emre Yusuf\",\"Jayabrata Bhaduri\"]","published":"2026-07-10T17:59:45Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\",\"cs.AI\",\"cs.LG\",\"eess.SP\",\"math.AT\"]","methods":"[\"LoRA\"]","has_code":false}